A new Alexandria scholarship fund, dedicated to providing "last dollar" assistance for city high school graduates pursuing their education, has launched a drive to raise $100,000 by next June.

The campaign will be given a boost Tuesday night by the City Council, which is expected to contribute $25,000 if that amount is matched by the community.

The Scholarship Fund of Alexandria, created a year ago in a joint effort by the community and school system personnel, is distinct from other scholarships in the city in that its prime purpose is to give several small grants to students whose postsecondary education is jeopardized because their financial aid does not cover their education costs.

Grants will vary in amount from between $500 and $1,000, said the fund's director, Kitty Porterfield.

In its first year of operation, the fund received $35,000 in gifts, without any fund raising. "It just walked through the door," said Porterfield, who works in an office on the grounds of the city's T.C. Williams High School.

In June, the fund assisted 16 members of T.C. Williams' graduating class with grants totaling $9,265.

Traditionally, 70 percent of T.C. Williams' graduating seniors continue their education. According to surveys, 64 percent of the financial cost for this comes from family and student incomes, with most of the rest coming from loans.

But rising costs of education and decreasing federal aid for students is putting an increasingly heavy burden on these families.

In addition, although Alexandria has one of the highest median incomes among the region's jurisdictions, 35 percent of the city's students qualify for free or reduced-price school lunches, indicating a financial need among many of its students. In 1987, the rate of the graduating class applying for financial aid increased from 18 percent to 21.

The fund is based on programs in Cleveland and Boston. Like them, the Alexandria program offers parents and students counseling on how to obtain other loans and grants, extending their access to such assistance. Both the Cleveland and Boston programs have shown that for every scholarship dollar they award, students have obtained $10 in aid from other sources because of this informational function.

The Cleveland program, created 20 years ago, "has seen its graduates break the poverty cycle in hundreds of families," its executive director, Clarence W. Mixon wrote in a letter to the Alexandria program.

To qualify for one of the fund's grants, a student must reside in Alexandria, pursue postsecondary education at a college, university or trade school, have a grade point average of at least 2.0 and display financial need. Grants may be renewed.

Porterfield said the $100,000 the fund hopes to raise will be used to create an endowment, whose interest will pay for grants for between 80 and 100 students.

The fund is under the direction of a board of trustees of Alexandria residents headed by Lou Cook, a former School Board chairman. Contributions are tax-deductible.

"I think it's important," Lou Cook said of the fund, because it will help "the kid who's been overlooked . . . the kid in the middle. He's not going to go to Harvard on a merit scholarship and he's not going to get money {from the government} because his family is not below the poverty line."